September 17th, 2013, 10:46 PM  #1 
Member Joined: Sep 2013 Posts: 33 Thanks: 0  The empty set
If P(A) is the power set of A=[a,b] and we no that B is a nonempty subset of A does B might be the empty set ? On one hand I just said the B is nonempty, on the other P(A) includes the empty set, so being the empty set B still includes an actual element of P(A). I am confused. Thank you. 
September 18th, 2013, 01:07 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: The empty set
First, the empty set is a subset of any set. But, this doesn't mean that it contains any element of the set. Here's an example that may help: Suppose you have a choice of a Coke or a Sprite. You actually have four options: You could drink the Coke. You could drink the Sprite. You could be greedy and drink both! Or, you could drink neither. This last option (not to choose anything that is available) is logically the same as the empty set being a subset of any set. 
September 19th, 2013, 06:32 AM  #3  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: The empty set Quote:
Had you just said "B is a subset of A" or "B is a member of P(A)" then B might well be empty. Yes, P(A) includes the empty set but that has nothing to do with "includes an actual element of A". (Another confusion "actual elements of P(A)", which is what you wrote, are subsets of A. "Subsets of A" do NOT generally contain other subsets of A.) You may be confused about the definition of "subset of A". Saying that "B is a subset of A" does NOT necessarily mean B "includes an actual element of A". B is a subset of A if B does NOT include any element that is NOT in A. Since the empty set does NOT include any elements, it cannot include any that are "not in A" and so is a subset of any set, A. P(A) is the set of all subsets of A, NOT just "all nonempty subsets of A" and always includes the empty set.  
September 22nd, 2013, 08:32 PM  #4 
Member Joined: Sep 2013 Posts: 33 Thanks: 0  Re: The empty set
Thanks, my question was indeed confusing as i wanted to ask if b may contain the emty set i learned that the answer isnpositive. Thanks again

September 25th, 2013, 03:47 PM  #5  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: The empty set Quote:
 

Tags 
empty, set 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Family of empty sets  Vasily  Applied Math  2  August 19th, 2012 12:31 PM 
Empty Set proof  jstarks4444  Applied Math  1  October 12th, 2011 05:40 PM 
empty set  outsos  Applied Math  36  April 30th, 2010 10:46 AM 
Empty set question  z0r  Applied Math  2  December 6th, 2008 08:58 PM 
Empty Set proof  jstarks4444  Number Theory  0  December 31st, 1969 04:00 PM 